In data storage and data communication environments, to maximize the storage capacity for a given volume of recording medium, and to maximize the rate of data transmission, it is desirable that the written bits have as high an information density as possible. As the information density increases, however, regions of data symbols increase their “interference” with both the writing and recovery of neighboring symbols. Without careful compensation for such interference, information may be distorted or lost. While it is possible to compensate for this inter-symbol-interference (ISI) after readout, it is most desirable to compensate for ISI before recording to minimize noise enhancement resulting from data passing through the system.
Description of Linear and Nonlinear ISI
Mathematically, ISI can be classified into two types: 1) linear ISI and 2) nonlinear ISI. Equation (1) formalizes this definition.             y      ⁢              (        t        )              =                  h        0            +                        ∑                      n            =            1                    ∞                ⁢                                   ⁢                              ∫                          -              ∞                                      +              ∞                                ⁢                      …            ⁢                                          ∫                                  -                  ∞                                                  +                  ∞                                            ⁢                                                                    h                    n                                    ⁢                                      (                                                                  τ                        1                                            ,                      …                      ⁢                                                                                           ,                                              τ                        n                                                              )                                                  ⁢                                  x                  ⁢                                      (                                          t                      -                                              τ                        1                                                              )                                                  ⁢                                                                   ⁢                …                ⁢                                                                   ⁢                                  x                  ⁢                                                                           ⁢                                      (                                          t                      -                                              τ                        n                                                              )                                                  ⁢                                  ⅆ                  τ                                                                          ⁢         
Here, the input time function x(t) is related to the output y(t) of a nonlinear system by a Volterra series with kernels hn and additive zero-mean random noise η(t). If the relationship between the input x(t) and output y(t) is linear, the first two terms containing h0 and h1(τ) are all that are necessary to completely describe the system. If the relationship between input and output includes nonlinear ISI, additional terms are necessary to describe the relationship.
Because of the increased computational complexity of processing or removing nonlinear distortions in a data storage system, it is desirable to make the system behave like a linear channel. In a linear channel, the relationship between the data input and the recovered signal can be completely described by a convolution of a linear filter with the input plus some additive random noise. From a coding and signal processing perspective, linearity is also desirable because historically there is a massive amount of theoretical work completed using linear channels. If a system can be made to behave linearly, the techniques and knowledge resulting from this large body of work can then be applied.
In one embodiment of a multi-level (ML) optical data storage system, a long track is divided into a large number of small regular data cells. A laser is used to either write to or read from the individual cells. In such an optical storage system, a primary source of inter-symbol-interference (ISI) is the size of the reading and writing laser beams. As the data cells are packed together, the effects of neighboring symbols on both the formation and recovery of the data cells increases. During read-back, the reading laser beam illuminates a region of material that contains more than one data cell. As a result, the signal associated with the data cell of interest includes a linear convolution of signals from its neighbors.
During the writing process, effects such as thermal diffusion and the overlap from the tails of a Gaussian recording laser beam modify the state and response of neighboring cells. These effects produce nonlinear ISI. Diffraction effects (which are linear in amplitude, not intensity) also contribute to nonlinear ISI, as do non-ideal effects related to the read-back process such as the nonlinearity of the photodiode and amplifiers. As a result of the above sources of ISI, the recovered data signal from a high-density recording and read-back system is corrupted by linear ISI, nonlinear ISI, and noise.
Variation in the recording process due to systematic variation of either the media response or the writing process also corrupts the recovered data signal. For example, variation of the size and shape of the reading beam during read-back may change the amount of inter-symbol-interference. Variation in the sensitivity of the media during recording may change the size and shape of the recorded marks. Because these effects result in a systematic or deterministic source of error, the impact of many of these error sources could potentially be minimized through careful write compensation.
Shaping the Channel
FIG. 1A is a diagram illustrating Shannon's original abstraction of a general communication system. An information source 102 generates a signal x(t) that is transmitted by a transmitter 104 through the system or “channel” 106 to receiver 108 and a final destination 110. Along the path from the information source 102 to the destination 110, the transmitted signal may be corrupted by both deterministic and random transformations. For example, a random noise source 112 is shown as an input to channel 106. It is the goal of the transmitter 104 in a communication or storage system to compensate for the effects of such corruption. For example, a transmitter in a robust information system will add redundancy to combat the particular noise structure involved.
It would be useful if a way could be provided to write compensate for deterministic transformations that occur in the channel. Write compensation refers to compensation that occurs during the writing process. Read compensation refers to compensation that occurs during the reading process. Compensation in general may occur during the writing process and/or during the reading process.
If a particular reading system design can only recover data that have undergone a linear transformation, then any nonlinear transformation may be classified as noise. It would be desirable to remove as many deterministic sources of such “noise” as possible using write compensation so that a reading system designed to compensate for linear transformations by the channel may be used effectively.
In general, both read and write compensation techniques are needed to maintain an acceptable signal to noise ratio (SNR) as information density increases on a storage medium. To the extent that write compensation can be used to cause the channel output to be linear or to conform to some desired target, the reading system may be simplified. Also, techniques are needed for compensating for transformations caused by various sources such as physical variations in a recording device or recording material response that occur as a result of manufacturing, wear, or environmental conditions.